The Annual Review of Fluid Mechanics covers the significant developments in the
field of fluid mechanics; its 2012 impact factor is 12.600.

Project synopsis

During my doctoral work, I initiated a system-theoretic approach to model and
analyze shear flows of Newtonian fluids, such as air and water. Using this
approach I obtained a detailed characterization of the flow structures
triggering the transition to turbulence. This is likely to have an impact in a
variety of applications including design of fuel-efficient and
environmentally-friendly vehicles. Since joining the University of Minnesota, I
used this early success as a motivation for a new line of research; this effort
resulted in a set of well developed theoretical and computational methods for
analysis and control of both Newtonian and non-Newtonian fluids.

In a recent interdisciplinary collaborative effort with Prof. Satish Kumar of
Chemical Engineering and Materials Science Department at the University of
Minnesota, I have been studying transition to turbulence in shear flows of
fluids containing long, flexible, polymer chains. Transition phenomena in these
complex viscoelastic fluids are relevant for polymer processing operations and
mixing in micro/nano-fluidic devices. Even though such flows are inherently
stable when inertial effects are negligible, they often exhibit deviations from
laminar profiles impairing quality of polymer products. My research has
demonstrated that these deviations are triggered by high flow sensitivity. To
counter this sensitivity I have explicitly accounted for modeling imperfections
by quantifying their influence on transient and asymptotic dynamics of
viscoelastic fluids. My work was the first to reveal previously unknown
structural similarities between weakly-inertial flows of viscoelastic fluids and
strongly-inertial flows of Newtonian fluids (see figure below for an
illustration) and is enhancing the understanding of the early stages of
transition to elastic turbulence.

Figure 1: Block diagrams of the frequency response operators that map the
wall-normal and spanwise forces to the streamwise velocity fluctuation in
streamwise-constant (a) inertialess flows of viscoelastic fluids; and (b)
inertial flows of Newtonian fluids. In Newtonian fluids amplification originates
from vortex tilting, i.e. the operator , and in viscoelastic
fluids it originates from polymer stretching, i.e. the operator
. Note that the Weissenberg number, , in
inertialess flows of viscoelastic fluids takes the role of the Reynolds number,
, in inertial flows of Newtonian fluids. Here, is the temporal
frequency, is the viscosity ratio, and and
are the streamwise-constant Orr-Sommerfeld and Squire
operators.